Question

ues eulid s division algorithm to the hcf of 135 and 225

Answer 1

(i) 135 and 225
Since 225 > 135, we apply the division lemma to 225 and 135 to obtain
225 = 135 × 1 + 90
Since remainder 90 ≠ 0, we apply the division lemma to 135 and 90 to obtain
135 = 90 × 1 + 45
We consider the new divisor 90 and new remainder 45, and apply the division lemma to obtain
90 = 2 × 45 + 0
Since the remainder is zero, the process stops.
Since the divisor at this stage is 45,
Therefore, the HCF of 135 and 225 is 45.

Answer 2

$a = bq + r \: \: \: where \: r \leqslant 0 \leqslant b \\ 225 = 135 \times 1 + 90 \\ 135 = 90 \times 1 + 45 \\ 90 = 45 \times 2 + 0 \\ the\: remainder \: has \: now \: become \: zero \\ hcf= 45$